# What is the cross product of [3,1,-4] and [1,1,18]

What is the cross product of [3,1,-4] and [1,1,18]
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SaphypycleDapc5
The vector cross product of two 3-dimesnional vectors in the vector space ${\mathbb{R}}^{3}$ may be computed as a matrix determinant
$\left(3,1,-4\right)×\left(1,1,18\right)=\left[\begin{array}{ccc}\stackrel{\to }{i}& \stackrel{\to }{j}& \stackrel{\to }{k}\\ 3& 1& -4\\ 1& 1& 18\end{array}\right]$
$=\stackrel{\to }{i}\left(18+4\right)-\stackrel{\to }{j}\left(54-1\right)+\stackrel{\to }{k}\left(3-1\right)$
$=22\stackrel{\to }{i}-\stackrel{\to }{j}53+2\stackrel{\to }{k}$
$=\left(22,-53,2\right)$